def _pred_sig(self, theta, phi, beta, lambda1, lambda2):
"""
The predicted signal for a particular setting of the parameters
"""
Q = np.array([[lambda1, 0, 0],
[0, lambda2, 0],
[0, 0, lambda2]])
# If for some reason this is not symmetrical, then something is wrong
# (in all likelihood, this means that the optimization process is
# trying out some crazy value, such as nan). In that case, abort and
# return a nan:
if not np.allclose(Q.T, Q):
return np.nan
response_function = ozt.Tensor(Q,
self.bvecs[:,self.b_idx],
self.bvals[:,self.b_idx])
# Convert theta and phi to cartesian coordinates:
x,y,z = geo.sphere2cart(1, theta, phi)
bvec = [x,y,z]
evals, evecs = response_function.decompose
rot_tensor = ozt.tensor_from_eigs(
evecs * ozu.calculate_rotation(bvec, evecs[0]),
evals, self.bvecs[:,self.b_idx], self.bvals[:,self.b_idx])
iso_sig = np.exp(-self.bvals[self.b_idx][0] * lambda1)
tensor_sig = rot_tensor.predicted_signal(1)
return beta * iso_sig + (1-beta) * tensor_sig
def _pred_sig(self, theta, phi, beta, lambda1, lambda2):
"""
The predicted signal for a particular setting of the parameters
"""
Q = np.array([[lambda1, 0, 0], [0, lambda2, 0], [0, 0, lambda2]])
# If for some reason this is not symmetrical, then something is wrong
# (in all likelihood, this means that the optimization process is
# trying out some crazy value, such as nan). In that case, abort and
# return a nan:
if not np.allclose(Q.T, Q):
return np.nan
response_function = ozt.Tensor(Q, self.bvecs[:, self.b_idx],
self.bvals[:, self.b_idx])
# Convert theta and phi to cartesian coordinates:
x, y, z = geo.sphere2cart(1, theta, phi)
bvec = [x, y, z]
evals, evecs = response_function.decompose
rot_tensor = ozt.tensor_from_eigs(
evecs * ozu.calculate_rotation(bvec, evecs[0]), evals,
self.bvecs[:, self.b_idx], self.bvals[:, self.b_idx])
iso_sig = np.exp(-self.bvals[self.b_idx][0] * lambda1)
tensor_sig = rot_tensor.predicted_signal(1)
return beta * iso_sig + (1 - beta) * tensor_sig
def test_Tensor_decompose():
"""
Test the eigen-vector/value decomposition of the tensor:
"""
q = np.array([
[1.5, 0, 0],
[0, 0.5, 0], # This needs to be slightly higher, so that
# there is no ambiguity about the order of the
# evals
[0, 0, 0.5]
])
# And the bvecs are unit vectors:
bvecs = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
bvals = [1, 1, 1]
T1 = mtt.Tensor(q, bvecs, bvals)
vals, vecs = T1.decompose
npt.assert_equal(vecs, np.eye(3))
npt.assert_equal(vals, np.diag(q))
T2 = mtt.tensor_from_eigs(vecs, vals, bvecs, bvals)
npt.assert_equal(T2.Q, q)
def _tensor_helper(self, theta, phi):
"""
This code is used in all three error functions, so we write it out
only once here
"""
# Convert to cartesian coordinates:
x, y, z = geo.sphere2cart(1, theta, phi)
bvec = [x, y, z]
# decompose is an auto-attr of the tensor object, so is only run once
# and then cached:
evals, evecs = self.response_function.decompose
rot = ozu.calculate_rotation(bvec, evecs[0])
rot_evecs = evecs * rot
rot_tensor = ozt.tensor_from_eigs(rot_evecs, evals,
self.bvecs[:, self.b_idx],
self.bvals[self.b_idx])
return rot_tensor
def _tensor_helper(self, theta, phi):
"""
This code is used in all three error functions, so we write it out
only once here
"""
# Convert to cartesian coordinates:
x,y,z = geo.sphere2cart(1, theta, phi)
bvec = [x,y,z]
# decompose is an auto-attr of the tensor object, so is only run once
# and then cached:
evals, evecs = self.response_function.decompose
rot = ozu.calculate_rotation(bvec, evecs[0])
rot_evecs = evecs * rot
rot_tensor = ozt.tensor_from_eigs(rot_evecs,
evals,
self.bvecs[:,self.b_idx],
self.bvals[:,self.b_idx])
return rot_tensor
def test_Tensor_decompose():
"""
Test the eigen-vector/value decomposition of the tensor:
"""
q = np.array([[1.5,0,0],
[0,0.5,0], # This needs to be slightly higher, so that
# there is no ambiguity about the order of the
# evals
[0,0,0.5]])
# And the bvecs are unit vectors:
bvecs = np.array([[1,0,0],[0,1,0],[0,0,1]])
bvals = [1,1,1]
T1 = mtt.Tensor(q, bvecs, bvals)
vals, vecs = T1.decompose
npt.assert_equal(vecs , np.eye(3))
npt.assert_equal(vals, np.diag(q))
T2 = mtt.tensor_from_eigs(vecs, vals, bvecs, bvals)
npt.assert_equal(T2.Q,q)
